Remark 2.2 
Let \(\alpha _{1},\alpha _{2} \in \mathbb {R}\) , \(\lbrace \alpha ^{1}_{k}\rbrace =\lbrace 2^{k\alpha _{1}}\rbrace \) , \(\lbrace \alpha ^{2}_{k}\rbrace =\lbrace 2^{k\alpha _{2}}\rbrace \) .
If under these assumptions one requires that conditions (2.3), (2.4) were satisfied for the weight sequence \(\lbrace \overline{t}_{k}\rbrace \)  (instead of \(\lbrace t_{k}\rbrace \) ), then
Definition REF  is equivalent to the corresponding definition from [1]}.

